in \({K}\) , where the map \(B\rightarrow \mathrm {Map}(K,B)\)  is the adjoint of \(B\times K\rightarrow B\) .
Recall also (see [1]}) that \({K}/B\)  is cartesian closed
under the fiberwise cartesian product \(X\times _B Y\)  and the fiberwise mapping space \(\mathrm {Map}_B(X,Y)\)  over \(B\) .
The definition of the fiberwise mapping space \(\mathrm {Map}_B(X,Y)\) 
is rather subtle and we will not give it here, we instead refer the reader to Definition 1.37 of [1]}.
Let us note though that \(\mathrm {Map}_B(X,Y)\)  is generally not weak Hausdorff even if
\(X\)  and \(Y\)  are, which is one of the main reasons why May and Sigurdsson choose to
work with the category \({K}/B\)  rather than the category \({U}/B\) .
